In my recent conversation about an experimental new app by Google, I noticed that their Android app is basically just a wrapper around their web app without any additional functionality:
Having seen that, I wondered if that might be a model for Cake as well: Don't try to build everything from scratch, but just start small with an app that is basically an instance of Google Chrome without the UI. In Android terms, what you need is a WebView, and this page describes how it's done:
Not having worked with WebView before, I gave it a try and ended up with a mostly functional Android app that could be put on the Play Store just an hour later.
The app could be expanded from there by replacing parts of the web experience with native UI elements as time allows - for example starting with Cake's navigation bar and replacing it with a native app bar. In order to do so, WebView allows to set a custom user agent string that could be used by the server to serve a variant of the regular content (in the above example, pages that don't include navigation). It could also be used to at least add notifications or better ways to share content to Cake:
Even if time does not allow in the foreseeable future, having at least some presence on Google's Play Store is probably better than nothing.